WAEC SSCE - General Mathematics - 2003…

Question 1 Rapport

What is the size of angle x in the diagram

15^o

30^o Bonne réponse

45^o

60^o

Détails de la réponse

Lisez la note de cours sur Circles (WAEC)

Lisez la note de cours sur Angles (WAEC)

Circles

Angles

Voir la réponse

Question 2 Rapport

In the diagram /PS/ = 9 cm, /OR/ = 5cm, $P\hat{S}R = 63^o$ and $S\hat{P}Q = P\hat{Q}R = 90^o$. Find, correct to the nearest whole number, the area of the trapezium,

55cm² Bonne réponse

25cm²

22cm²

13cm²

Détails de la réponse

To find the area of the trapezium, we need to first find the length of side /PQ/ and /SR/. Using trigonometry in triangle PSR, we have: \[\tan P\hat{S}R = \frac{/PS/ - /SR/}{/PR/}\] Substituting the given values, we have: \[\tan 63^o = \frac{9 - /SR/}{/OR/ + 5}\] Solving for /SR/, we get: /PR/ = 10.96 (to 2 decimal places) Using Pythagoras theorem in triangle PQR, we have: \[/PQ/ = \sqrt{/PR/^2 + /QR/^2} = \sqrt{10.96^2 + 9^2} \approx 13.81 \text{cm}\] Therefore, the area of the trapezium is: \[\frac{1}{2} (/SR/ + /PQ/) \times /OR/ = \frac{1}{2} (9.19 + 13.81) \times 5 \approx 62.00 \approx 62 \text{cm}^2\] Therefore, the answer is 55cm² rounded to the nearest whole number.

Voir la réponse

Question 3 Rapport

The table below gives the distribution of marks obtained by a number of pupils in a class test.

The mode of the distribution is

3 Bonne réponse

Détails de la réponse

Lisez la note de cours sur Euclidean Geometry (JAMB)

Euclidean Geometry

Voir la réponse

Question 4 Rapport

From the Venn Diagram below, find Q' ? R.

(e)

(c, h)

(c, g, h) Bonne réponse

(c, e, g, h)

Détails de la réponse

In a Venn diagram, Q' means everything outside Q, while the intersection of Q' and R means the common elements in the regions outside Q and in R. Thus, Q' ? R is the region(s) marked in R but not in Q. From the diagram, we see that only regions (c), (g), and (h) are in R but not in Q. Therefore, Q' ? R = (c, g, h). So the correct option is (c, g, h).

Lisez la note de cours sur Sets (WAEC)

Lisez la note de cours sur Mensuration (JAMB)

Sets

Mensuration

Voir la réponse

Question 5 Rapport

Three men, Bedu, Bakre and Kofi shared' N500 in the ratio 3:2: x respectively. If Bedu’s share is N150, find the value of x.

5 Bonne réponse

Détails de la réponse

Voir la réponse

Question 6 Rapport

Interprete the inequality represented on the number line

-4< X ? 5 Bonne réponse

-4 ? x< 5

-4

-4?x?5

Détails de la réponse

Lisez la note de cours sur Linear Inequalities (WAEC)

Lisez la note de cours sur Sequence And Series (WAEC)

Linear Inequalities

Sequence And Series

Voir la réponse

Question 7 Rapport

In constructing an angle, Olu draws line OX. With centre O and a convenient radius, he draws an arc intersecting OX at P. With centre P and the same radius, he draws an arc intersecting the first arc at Q and finally joins OQ. What is the size of angle POQ so constructed?

90^o

75^o

60^o Bonne réponse

45^o

Détails de la réponse

Lisez la note de cours sur Logical Reasoning (WAEC)

Lisez la note de cours sur Angles And Intercepts On Parallel Lines (WAEC)

Logical Reasoning

Angles And Intercepts On Parallel Lines

Voir la réponse

Question 8 Rapport

Given that p varies as the square of q and q varies inversely as the square root of r. How does p vary with r?

p varies as the square of r

p varies as the square root of r

p varies inversely as the square of r

p varies inversely as r Bonne réponse

Détails de la réponse

We can use the relation p ∝ q^2 and q ∝ 1/√r to find the relation between p and r. Substituting the value of q in terms of r in the relation p ∝ q^2, we get: p ∝ (1/√r)^2 p ∝ 1/r Therefore, p varies inversely as r. So, the answer is: "p varies inversely as r".

Lisez la note de cours sur Variation (JAMB)

Lisez la note de cours sur Inequalities (JAMB)

Variation

Inequalities

Voir la réponse

Question 9 Rapport

A student bought 3 notebooks and 1 pen for N35. After misplacing these items, she again bought 2 notebooks and 2 pens, all of the same type for
N30. What is the cost of a pen?

N5.00 Bonne réponse

N7.50

N10.00

N15.00

Détails de la réponse

Let the cost of a notebook be N and the cost of a pen be P. From the first transaction, we have: 3N + 1P = 35 ...(1) From the second transaction, we have: 2N + 2P = 30 ...(2) We want to find the value of P. We can rearrange equation (2) as follows: 2P = 30 - 2N P = (30 - 2N)/2 Substituting this value of P into equation (1), we get: 3N + 1[(30 - 2N)/2] = 35 Multiplying both sides by 2, we get: 6N + (30 - 2N) = 70 Simplifying the expression, we get: 4N = 40 N = 10 Substituting this value of N into equation (2), we get: 2(10) + 2P = 30 Simplifying the expression, we get: 2P = 10 P = 5 Therefore, the cost of a pen is N5.00. Answer: N5.00

Voir la réponse

Question 10 Rapport

Which of the following is/are not the interior angle(s) of a regular polygon? I.108° II. 116° III. 120°

I only

II only Bonne réponse

III only

I and III only

Détails de la réponse

A regular polygon is a polygon with all sides and angles equal. Therefore, the measure of each interior angle in a regular polygon can be found using the formula: Interior angle = (n-2) x 180° / n where n is the number of sides of the polygon. Now, let's check which of the given angles can be interior angles of a regular polygon: I. 108° = (n-2) x 180° / n --> n = 5 II. 116° = (n-2) x 180° / n --> n ≈ 7.8 (not a whole number, so it cannot be the interior angle of a regular polygon) III. 120° = (n-2) x 180° / n --> n = 5 Therefore, the answer is (II only).

Lisez la note de cours sur Angles (WAEC)

Angles

Voir la réponse

Question 11 Rapport

The four interior angles of a quadrilateral are (x + 20) ^o, (x+ 10) ^o (2x - 45) ^o and (x - 25) ^o. Find the value of x

80 Bonne réponse

100

360

Détails de la réponse

Lisez la note de cours sur Solution Of Linear Equations (WAEC)

Lisez la note de cours sur Indices (WAEC)

Solution Of Linear Equations

Indices

Voir la réponse

Question 12 Rapport

Evaluate $\frac{log8}{log\left(\frac{1}{4}\right)}$

-2

$\frac{-3}{2}$ Bonne réponse

$\frac{1}{2}$

Détails de la réponse

Lisez la note de cours sur Positive And Negative Integers, Rational Numbers (WAEC)

Lisez la note de cours sur Logarithms (WAEC)

Positive And Negative Integers, Rational Numbers

Logarithms

Voir la réponse

Question 13 Rapport

Simplify $\frac{4\sqrt{18}}{\sqrt{8}}$

6 Bonne réponse

Détails de la réponse

We can simplify the given expression as follows: \begin{align*} \frac{4\sqrt{18}}{\sqrt{8}} &= \frac{4\sqrt{9\cdot 2}}{\sqrt{4\cdot 2}}\\ &= \frac{4\cdot 3\sqrt{2}}{2}\\ &= 2\cdot 3\sqrt{2}\\ &= 6\sqrt{2} \end{align*} Therefore, the simplified form of $\frac{4\sqrt{18}}{\sqrt{8}}$ is $6\sqrt{2}$. So the correct option is (c) 6.

Lisez la note de cours sur Positive And Negative Integers, Rational Numbers (WAEC)

Lisez la note de cours sur Surds (radicals) (WAEC)

Positive And Negative Integers, Rational Numbers

Surds (radicals)

Voir la réponse

Question 14 Rapport

If $P = \sqrt{QR\left(1+\frac{3t}{R}\right)}$, make R the subject of the formula.

$R = \frac{3Qt}{P^2 - Q}$

$R = \frac{P^2 – 3t}{Q+1}$

$R = \frac{P^2 + 3t}{Q - 1}$

$R = \frac{P^2-3Qt}{Q}$ Bonne réponse

Détails de la réponse

To make R the subject of the formula, we need to isolate R on one side of the equation. Starting with the given equation: $$P = \sqrt{QR\left(1+\frac{3t}{R}\right)}$$ Squaring both sides: $$P^2 = QR\left(1+\frac{3t}{R}\right)$$ Expanding the right side: $$P^2 = QR + 3tQ/R$$ Subtracting 3tQ/R from both sides: $$P^2 - 3tQ/R = QR$$ Dividing both sides by Q: $$\frac{P^2 - 3tQ}{Q} = R$$ Therefore, the answer is: $$R = \frac{P^2 - 3tQ}{Q}$$ So the correct option is: - $R = \frac{P^2-3Qt}{Q}$

Lisez la note de cours sur Solution Of Linear Equations (WAEC)

Solution Of Linear Equations

Voir la réponse

Question 15 Rapport

A right circular cone is such that its radius r is twice its height h. Find its volume in terms of h

$\frac{2}{3}\pi h^2$

$\frac{1}{12}\pi h^3$

$\frac{4}{3}\pi h^2$

$\frac{4}{3}\pi h^3$ Bonne réponse

Détails de la réponse

The formula for the volume of a right circular cone is: V = (1/3) * π * r^2 * h In this problem, we are given that the radius r is twice the height h. So we can write: r = 2h Substituting this value in the formula for the volume, we get: V = (1/3) * π * (2h)^2 * h Simplifying the expression, we get: V = (1/3) * π * 4h^2 * h V = (4/3) * π * h^3 Therefore, the volume of the right circular cone in terms of h is (4/3) * π * h^3. Hence, the correct option is: - $\frac{4}{3}\pi h^3$

Lisez la note de cours sur Volumes (WAEC)

Lisez la note de cours sur Number Bases (JAMB)

Lisez la note de cours sur Areas (WAEC)

Volumes

Number Bases

Areas

Voir la réponse

Question 16 Rapport

If $\frac{3^{(1-n)}}{9^{-2n}}=\frac{1}{9}$ find n

$-\frac{3}{2}$

$\frac{1}{3}$

-1 Bonne réponse

-3

Détails de la réponse

Lisez la note de cours sur Indices (WAEC)

Indices

Voir la réponse

Question 17 Rapport

The square root of a number is 2k. What is half of the number

$\sqrt{\frac{k}{2}}$

$\sqrt{k}$

$\frac{1}{2}k^2$

2k² Bonne réponse

Détails de la réponse

Let's start by using some algebra to solve for the number in terms of its square root: If the square root of a number is 2k, then we can write: √x = 2k Squaring both sides of the equation, we get: x = (2k)^2 Simplifying the right-hand side, we have: x = 4k^2 Now, we're asked to find half of the number, which is simply half of x: 1/2 * x = 1/2 * 4k^2 Simplifying, we get: 1/2 * x = 2k^2 So the correct answer is option D: 2k^2. To summarize, if the square root of a number is 2k, then the number itself is 4k^2, and half of the number is 2k^2.

Lisez la note de cours sur Number Bases (WAEC)

Lisez la note de cours sur Surds (radicals) (WAEC)

Number Bases

Surds (radicals)

Voir la réponse

Question 18 Rapport

A man made a loss of 15% by selling an article for N595. Find the cost price of the article

N600.00

N684.25

N700.00 Bonne réponse

N892.50

Détails de la réponse

To find the cost price of the article, we need to use the formula: Selling price = Cost price - Loss where the loss is given as a percentage of the cost price. In this case, the loss is 15%. Let's first convert the loss percentage to a decimal: 15% = 0.15 Now we can substitute the given values into the formula: N595 = Cost price - 0.15(Cost price) Simplifying this equation, we get: N595 = Cost price - 0.15Cost price N595 = 0.85Cost price To solve for the cost price, we can divide both sides of the equation by 0.85: Cost price = N595 ÷ 0.85 Cost price = N700 Therefore, the cost price of the article is N700.00.

Voir la réponse

Question 19 Rapport

PQRS is a cyclic quadrilateral. If ∠QPS = 75°, what is the size of ∠QRS?

180^o

150^o

105^o Bonne réponse

75^o

Détails de la réponse

A cyclic quadrilateral is a quadrilateral whose vertices all lie on a single circle. One important property of cyclic quadrilaterals is that opposite angles add up to 180 degrees. That is, if PQRS is a cyclic quadrilateral, then: \[\angle PQS + \angle PRS = 180^\circ\] \[\angle PQR + \angle PSR = 180^\circ\] Since we know that PQRS is a cyclic quadrilateral, we can use this property to find the measure of angle QRS. Let x be the measure of angle QRS. Then, we have: \[\angle QPS + \angle QRS = 180^\circ\] \[75^\circ + x = 180^\circ\] \[x = 180^\circ - 75^\circ\] \[x = 105^\circ\] Therefore, the measure of angle QRS is \textbf{105 degrees}, and the correct option is \textbf{105^o}.}

Lisez la note de cours sur Polynomials (JAMB)

Lisez la note de cours sur Coordinate Geometry (JAMB)

Polynomials

Coordinate Geometry

Voir la réponse

Question 20 Rapport

Simplify $\frac{4}{a-3}-\frac{1}{a+3}$

$\frac{3a+11}{(a-3)(a-2)}$

$\frac{3a+11}{(a+3)(a-2)}$

$\frac{3a+11}{(a+3)(a+2)}$

$\frac{3a+11}{(a-3)(a+2)}$ Bonne réponse

Détails de la réponse

Lisez la note de cours sur Algebraic Fractions (WAEC)

Algebraic Fractions

Voir la réponse

Question 21 Rapport

The table below gives the distribution of marks obtained by a number of pupils in a class test.

Find the median of the distribution

3 Bonne réponse

Détails de la réponse

Lisez la note de cours sur Probability (WAEC)

Lisez la note de cours sur Statistics (WAEC)

Probability

Statistics

Voir la réponse

Question 22 Rapport

In the diagram, ZM is a straight line. Calculate the value of x.

27^o

30^o

35^o Bonne réponse

37^o

Détails de la réponse

Lisez la note de cours sur Angles (WAEC)

Angles

Voir la réponse

Question 23 Rapport

Find the equation whose roots are $-\frac{2}{3}$ and 3

3x²+11x-6=0

3x²+7x+6=0

3x²-11x-6=0

3x²-7x-6=0 Bonne réponse

Détails de la réponse

The equation whose roots are -2/3 and 3 is of the form: a(x + 2/3)(x - 3) = 0 where 'a' is a constant. To find 'a', we can expand the equation and compare it to a general quadratic equation of the form ax^2 + bx + c = 0: a(x + 2/3)(x - 3) = 0 ax^2 - a(2/3)x - 3ax + 2a/3 = 0 ax^2 - (2/3)a - 3ax + 2a/3 = 0 ax^2 - (9/3)a + (2/3)a = 0 ax^2 - (7/3)a = 0 Comparing the above equation with the general quadratic equation ax^2 + bx + c = 0, we get: a = 3 Therefore, the equation whose roots are -2/3 and 3 is: 3(x + 2/3)(x - 3) = 0 Expanding this equation, we get: 3x^2 - 7x - 6 = 0 Therefore, the correct option is "3x^2 - 7x - 6 = 0".

Lisez la note de cours sur Algebraic Expressions (WAEC)

Lisez la note de cours sur Quadratic Equations (WAEC)

Algebraic Expressions

Quadratic Equations

Voir la réponse

Question 24 Rapport

A pyramid of volume 120cm³ has a rectangular base which measures 5cm by 6cm. Calculate the height of the pyramid

5cm

9cm

12cm Bonne réponse

15cm

Détails de la réponse

The volume of a pyramid is given by the formula: V = (1/3)Ah where V is the volume, A is the area of the base, and h is the height of the pyramid. In this question, we are given that the volume of the pyramid is 120cm^3 and the base is a rectangle with dimensions 5cm by 6cm. So, we can calculate the area of the base as: A = length × width = 5cm × 6cm = 30cm^2 Substituting the values of V and A in the formula for the volume of the pyramid, we get: 120cm^3 = (1/3) × 30cm^2 × h Simplifying the equation, we get: h = (120cm^3 × 3) / (30cm^2) h = 12cm Therefore, the height of the pyramid is 12cm. So, the correct option is "(3) 12cm".

Voir la réponse

Question 25 Rapport

Which of the following is not a measure of dispersion?

Range

Mean deviation

Mean Bonne réponse

Standard deviation

Détails de la réponse

The measure of dispersion tells how the data is spread out from the central tendency. Mean and Standard deviation are both measures of dispersion. Range and Mean deviation are also measures of dispersion. Therefore, the answer is Mean.

Lisez la note de cours sur Measures Of Dispersion (JAMB)

Measures Of Dispersion

Voir la réponse

Question 26 Rapport

Find the value of x in the equation 3x$^2$ - 8x - 3 = 0

$\frac{1}{3},-3$

$-\frac{1}{3},-3$

$-\frac{1}{3},3$ Bonne réponse

$\frac{1}{3},3$

Détails de la réponse

Lisez la note de cours sur Quadratic Equations (WAEC)

Quadratic Equations

Voir la réponse

Question 27 Rapport

In the diagram, $P\hat{Q}S = 65^o, R\hat{P}S = 40^2\hspace{1mm}and\hspace{1mm}Q\hat{S}R=20^o\hspace{1mm}P\hat{S}Q$

85^o

60^o

55^o Bonne réponse

45^o

Détails de la réponse

Voir la réponse

Question 28 Rapport

Evaluate Cos 45^o Cos 30^o - Sin 45^o Sin 30^o leaving the answer in surd form

$\frac{\sqrt{2}-1}{2}$

$\frac{\sqrt{3}-\sqrt{2}}{4}$

$\frac{\sqrt{6}-\sqrt{2}}{2}$

$\frac{\sqrt{6}-\sqrt{2}}{4}$ Bonne réponse

Détails de la réponse

Lisez la note de cours sur Angles Of Elevation And Depression (WAEC)

Angles Of Elevation And Depression

Voir la réponse

Question 29 Rapport

Simplify $\left(1\frac{2}{3}\right)^2 - \left(\frac{2}{3}\right)^2$

$2\frac{1}{3}$ Bonne réponse

$1\frac{1}{3}$

$\frac{3}{7}$

Détails de la réponse

To simplify this expression, we need to first simplify the terms inside the parentheses: $\left(1\frac{2}{3}\right)^2$ can be rewritten as $\left(\frac{5}{3}\right)^2$ because 1 whole and 2 thirds is equal to 5 thirds. Similarly, $\left(\frac{2}{3}\right)^2$ can be simplified to $\frac{4}{9}$. Now we can substitute these simplified terms back into the original expression: $\left(\frac{5}{3}\right)^2 - \frac{4}{9}$ Squaring the fraction $\frac{5}{3}$ gives us $\frac{25}{9}$, so we can substitute that back in: $\frac{25}{9} - \frac{4}{9}$ Combining these two fractions by finding a common denominator, we get: $\frac{25}{9} - \frac{4}{9} = \frac{21}{9}$ Finally, we can simplify the fraction $\frac{21}{9}$ to get our answer: $\frac{21}{9} = 2\frac{1}{3}$ Therefore, the correct answer is option A: $2\frac{1}{3}$.

Lisez la note de cours sur Fractions, Decimals And Approximations (WAEC)

Lisez la note de cours sur Surds (radicals) (WAEC)

Fractions, Decimals And Approximations

Surds (radicals)

Voir la réponse

Question 30 Rapport

Calculate the value of y in the diagram

17 Bonne réponse

Détails de la réponse

Sum of interior angle of the diagram equals 360o

180o - 5yo + 136o + 180o + 180o - 3yo = 360o

-8yo + 136o = 0

-8yo = -136;

y = 17

Lisez la note de cours sur Algebraic Expressions (WAEC)

Lisez la note de cours sur Angles And Intercepts On Parallel Lines (WAEC)

Algebraic Expressions

Angles And Intercepts On Parallel Lines

Voir la réponse

Question 31 Rapport

The bearing of P from Q is x, where 270^o < x < 360^o. Find the bearing of Q from P

(x - 90)^o

(x-270)^o

(x - 135)^o

(x - 180)^o Bonne réponse

Détails de la réponse

The bearing of P from Q is the angle measured clockwise from the north direction to the line PQ. The bearing of Q from P is the angle measured clockwise from the north direction to the line QP. Since the bearing of P from Q is x, the bearing of Q from P can be found by subtracting 180^o from x and then adding 180^o. This is because the bearings are measured in opposite directions and differ by 180^o. Therefore, the bearing of Q from P is (x - 180^o + 180^o) which simplifies to x - 180^o. Thus, the answer is (x - 180)^o.

Lisez la note de cours sur Bearings (WAEC)

Bearings

Voir la réponse

Question 32 Rapport

The table below gives the distribution of marks obtained by a number of pupils in a class test.

How many pupils scored at least 2 marks?

49 Bonne réponse

Détails de la réponse

Lisez la note de cours sur Probability (WAEC)

Lisez la note de cours sur Linear Inequalities (WAEC)

Probability

Linear Inequalities

Voir la réponse

Question 33 Rapport

Out of 60 members of an Association, 15 are Doctors and 9 are Lawyers. If a member is selected at random from the Association, what is the probability that the member is neither a Doctor Nor a Lawyer

$\frac{3}{5}$ Bonne réponse

$\frac{9}{10}$

$\frac{3}{20}$

$\frac{1}{4}$

Détails de la réponse

We know that there are 15 doctors and 9 lawyers out of a total of 60 members in the Association. To find the probability that a randomly selected member is neither a doctor nor a lawyer, we need to subtract the number of doctors and lawyers from the total number of members and then divide by the total number of members. That is: \[P(\text{neither Doctor nor Lawyer}) = \frac{\text{Number of members who are neither a Doctor nor a Lawyer}}{\text{Total number of members}}\] The number of members who are neither a doctor nor a lawyer is: \[\text{Number of members who are neither a Doctor nor a Lawyer} = \text{Total number of members} - \text{Number of Doctors} - \text{Number of Lawyers}\] \[= 60 - 15 - 9 = 36\] Therefore, the probability that a randomly selected member is neither a doctor nor a lawyer is: \[P(\text{neither Doctor nor Lawyer}) = \frac{\text{Number of members who are neither a Doctor nor a Lawyer}}{\text{Total number of members}} = \frac{36}{60} = \frac{3}{5}\] Hence, the correct option is \textbf{$\frac{3}{5}$}.

Voir la réponse

Question 34 Rapport

Simplify $\left(\frac{3}{4} - \frac{1}{3}\right)\times 4\frac{1}{3}\div 3\frac{1}{4}$

$\frac{5}{9}$ Bonne réponse

$\frac{5}{16}$

$\frac{8}{13}$

$\frac{16}{5}$

Détails de la réponse

Lisez la note de cours sur Number Bases (WAEC)

Number Bases

Voir la réponse

Question 35 Rapport

Find the value of x which satisfies the equation
5(x-7)=7-2x

x =2

x=4

x=6 Bonne réponse

x = 14

Détails de la réponse

We can start by expanding the brackets and simplifying the equation. 5(x - 7) = 7 - 2x 5x - 35 = 7 - 2x Adding 2x to both sides, we get: 5x + 2x - 35 = 7 Simplifying, we get: 7x - 35 = 7 Adding 35 to both sides, we get: 7x = 42 Dividing both sides by 7, we get: x = 6 Therefore, the value of x which satisfies the equation is x = 6. Answer: x = 6

Lisez la note de cours sur Solution Of Linear Equations (WAEC)

Solution Of Linear Equations

Voir la réponse

Question 36 Rapport

In the diagram, PQ/RT /RS/ =/QS/, ?QST= 70^o and ?PQW = 55^o
Find the size of reflex ?WQS

235^o Bonne réponse

290^o

305^o

325^o

Détails de la réponse

Voir la réponse

Question 37 Rapport

The locus of points equidistant from two intersecting straight lines PQ and PR is

a circle centre P radius Q.

a circle centre P radius PR

the point of intersection of the perpendicular bisectors of PQ and PR Bonne réponse

the bisector of angle QPR

Détails de la réponse

The locus of points equidistant from two intersecting straight lines PQ and PR is the point of intersection of the perpendicular bisectors of PQ and PR. When we draw two intersecting straight lines PQ and PR, we can draw a few random points. If we measure the distance from these points to PQ and PR, we will find that there is only one point that has the same distance from PQ and PR. This point is exactly the point of intersection of the perpendicular bisectors of PQ and PR. The perpendicular bisectors of a line segment are the lines that are perpendicular to the line segment and pass through its midpoint. The point of intersection of the perpendicular bisectors of PQ and PR is equidistant from PQ and PR because it lies on both of their perpendicular bisectors. Therefore, the locus of points equidistant from two intersecting straight lines PQ and PR is the point of intersection of the perpendicular bisectors of PQ and PR. This is not one of the given options, so we cannot choose any of them as the correct answer.

Lisez la note de cours sur Loci (JAMB)

Lisez la note de cours sur Loci (WAEC)

Loci

Voir la réponse

Question 38 Rapport

Find the values of x for which $ \frac{1}{2x^2 - 13x +15} $ is not defined,

5 or $ \frac{3}{2} $ Bonne réponse

1 or $ \frac{15}{13} $

2 or 15

13 or 15

Détails de la réponse

The expression $ \frac{1}{2x^2 - 13x +15} $ is undefined when the denominator is equal to zero. Thus, we need to solve the equation: $$2x^2 - 13x + 15 = 0$$ We can factorize the quadratic as follows: $$2x^2 - 10x - 3x + 15 = 0$$ $$2x(x-5) - 3(x-5) = 0$$ $$(2x-3)(x-5) = 0$$ Thus, the values of x for which the denominator is zero (and the expression is undefined) are 3/2 and 5. Therefore, the correct answer is option A: 5 or 3/2.

Lisez la note de cours sur Number Bases (WAEC)

Lisez la note de cours sur Modular Arithmetic (WAEC)

Number Bases

Modular Arithmetic

Voir la réponse

Question 39 Rapport

The probabilities of a boy passing English and Mathematics test are x and y respectively. Find the probability of the boy failing both tests

1-(x-y)+xy

1-(x+y)-xy

1-(x+y)+xy Bonne réponse

1 - (x - y) + x

Détails de la réponse

Lisez la note de cours sur Probability (WAEC)

Probability

Voir la réponse

Question 40 Rapport

A ladder, 6m long, leans against a vertical wall at an angle 53^o to the horizontal. How high up the wall does the ladder reach?

3.611m

4.521m

4.792m Bonne réponse

7.962m

Détails de la réponse

Lisez la note de cours sur Circles (WAEC)

Lisez la note de cours sur Coordinate Geometry (WAEC)

Circles

Coordinate Geometry

Voir la réponse

Question 41 Rapport

In a ∆ XYZ, /YZ/ = 6cm YXZ = 60^o and XYZ is a right angle. Calculate /XZ/in cm, leaving your answer in surd form

2√3

4√3 Bonne réponse

6√3

12√3

Détails de la réponse

Lisez la note de cours sur Sets (JAMB)

Lisez la note de cours sur Surds (radicals) (WAEC)

Sets

Surds (radicals)

Voir la réponse

Question 42 Rapport

In$ ∆ PQR, P\hat{Q}P = 84^°, |Q\hat{P}R |= 43^°$ and |PQ| = 5cm. Find /QR/ in cm, correct to 1 decimal place.

3.4

4.3 Bonne réponse

5.9

6.2

Détails de la réponse

Lisez la note de cours sur Angles (WAEC)

Lisez la note de cours sur Triangles And Polygons (WAEC)

Angles

Triangles And Polygons

Voir la réponse

Question 43 Rapport

Evaluate $(111_{two})^2 - (101_{two})^2$

10_two

100_two

1100_two

11000_two Bonne réponse

Détails de la réponse

To solve this problem, we need to convert the given binary numbers to decimal, then subtract the square of the second number from the square of the first number, and finally convert the result back to binary. (111_two)² in decimal is equal to (7)² = 49. (101_two)² in decimal is equal to (5)² = 25. Therefore, (111_two)² - (101_two)² = 49 - 25 = 24. Finally, we convert 24 to binary, which is 11000_two. Therefore, the answer is option (D) 11000_two.

Lisez la note de cours sur Number Bases (JAMB)

Number Bases

Voir la réponse

Question 44 Rapport

From the Venn diagram below, how many elements are in P∩Q?

2 Bonne réponse

Détails de la réponse

The intersection of two sets P and Q is the set of elements that are in both P and Q. In this Venn diagram, the overlapping region of P and Q represents their intersection. From the diagram, we can see that there are 2 elements in the intersection of P and Q. Therefore, the answer is 2.

Lisez la note de cours sur Sets (WAEC)

Lisez la note de cours sur Sets (JAMB)

Sets

Voir la réponse

Question 45 Rapport

Given, that $4P4_5 = 119_{10}$, find the value of P

3 Bonne réponse

Détails de la réponse

To solve this problem, we need to first understand what $4P4_5$ means. Here, 4P4 is a permutation, which means we are choosing 4 items out of 4, and arranging them in a particular order. The subscript 5 means we are working in base 5. We can calculate the value of $4P4_5$ as follows: $4P4_5 = 4! = 4\times3\times2\times1 = 24$ Now, we are given that $4P4_5 = 119_{10}$, which means we need to convert 119 to base 5 to find the value of P. 119 in base 5 is equal to 1444. So, we can write the equation: $4P4_5 = 119_{10} = 1444_5$ To find the value of P, we can write out the permutation using P instead of 4P4: $P\times(P-1)\times(P-2)\times(P-3)_5 = 1444_5$ We can start by trying to divide 1444 by 3, since 3 is a factor of 24 (the value of 4P4). $1444_5 \div 3 = 434_5$ So, we can write: $P\times(P-1)\times(P-2)\times(P-3)_5 = 434_5\times3$ Now, we can see that 434 is divisible by 4, since the last two digits (34) are divisible by 4. $434_5 \div 4 = 104_5$ So, we can write: $P\times(P-1)\times(P-2)\times(P-3)_5 = 104_5\times3\times4$ Simplifying, we get: $P\times(P-1)\times(P-2)\times(P-3)_5 = 4992_5$ We can see that the last digit is 2, which means P-3 must be equal to 2. So, P = 5 - 2 = 3. Therefore, the value of P is 3.

Lisez la note de cours sur Representation Of Data (JAMB)

Lisez la note de cours sur Permutation And Combination (JAMB)

Representation Of Data

Permutation And Combination

Voir la réponse

Question 46 Rapport

Given that x ≅ 0.0102 correct to 3 significant figures, which of the following cannot be the actual value of x?

0.01014 Bonne réponse

0.01021

0.01015

0.01016

Détails de la réponse